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# a ladder 15 metres long just reaches the top of a vertical wall. if the ladder makes an angle of 60° with the wall, then the height of the wall will be

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## A ladder 15 m long just reaches the top of a vertical wall If the ladder makes an angle of 60 with t...

Free solutions for Mathematics Exemplar Problems - class 10 Chapter 9 - Introduction to Trigonometry and Its Equations Introduction to Trigonometry and Its Equations - Exercise 8.3 question 4. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

## NCERT Exemplar Solutions Class 10 Mathematics Solutions for Introduction to Trigonometry and Its Equations - Exercise 8.3 in Chapter 8 - Introduction to Trigonometry and Its Equations

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A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

Consider the vertical wall WL = x m (let)

Length of inclined ladder AW = 15 m ...[Given]

Ladder makes an angle of 60° with the wall.

\begin{array}{l} \therefore \frac{x}{15}=\cos 60^{\circ} \\ \Rightarrow \frac{x}{15}=\frac{1}{2} \\ \Rightarrow x=\frac{15}{2}=7.5 \end{array}

∴ 15 x ​ =cos60 ∘ ⇒ 15 x ​ = 2 1 ​ ⇒x= 2 15 ​ =7.5 ​

Hence, the height of the wall = 7.5 m.

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## A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘ with the wall, then find the height of the wall.

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘ with the wall, then find the height of the wall.

Byju's Answer Standard X Mathematics Angle of Elevation A ladder 15 m... Question

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of

60 ∘

with the wall, then find the height of the wall.

Open in App Solution

Given that, the height of the ladder = 15 m

Let the height of the vertical wall = h

And the ladder makes an angle of elevation

60 ∘ with the wall i.e., θ = 60 ∘ In Δ Q R P , cos 60 ∘ = P R P Q = h 15 ⇒ 1 2 = h 15 [ ∵ cos 60 ∘ = 1 2 ] ⇒ h = 15 2 = 7.5 m

Hence, the required height of the wall is

15 2 = 7.5 m . Suggest Corrections 41 Video Solution

EXEMP - Grade 10 - MATHEMATICS - Introduction to Trigonometry and its Applications - Q37

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SIMILAR QUESTIONS

Q.

A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of

60 ∘

with the wall, find the height of the wall.

Q. Question 15

Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

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## A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^∘ with the wall. Find the height of the wall.

Click here👆to get an answer to your question ✍️ A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^∘ with the wall. Find the height of the wall.

A ladder 15m long just reaches the top of a vertical wall. If the ladder makes an angle of 60

Question ∘

with the wall. Find the height of the wall.

Hard Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Let the length of the ladder be =15m(hypotenuse)

The angle between the ladder and the wall ∠BCA=60

Angle between ladder and the ground ∠CAB=90

∘ −60 ∘ =30 ∘

Height of the wall =BC

sin30 ∘ = 15 BC ​ ⇒ 2 1 ​ = 15 BC ​ ⇒BC= 2 15 ​ =7.5m

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